By contrast, the EU benefits from buying things from and selling things to the UK. Products made in the UK did not suddenly become less safe because of Brexit.
English economist David Ricardo made a similar statement in the early 19th century. The example he used was Portuguese wine being traded for English cloth. He said both countries benefited from their specializations - England producing cloth, Portugal producing wine. Ricardo's work is a foundation for a modern view of comparative advantage and free trade.
English economist Joan Robinson revisited this example over a century later. She asked what the results over the past century were for the economies of England and Portugal in pursuing this course - one country industrializing to build textile mills, one country remaining more agricultural with much less industrialization. I'm sure I don't have to tell you what she found in that investigation, the answer is obvious.
Sometimes upon finding a flaw in an analogy it is at least self-instructive to consider whether the flaw can be repaired rather than abandoned :: sometimes upon finding a flaw in a cooperative venture it is at least worth considering how the flaw can be repaired rather than withdrawing from the cooperative venture.
Analogies are perfectly fine ways to throw away superfluous detail to focus on salient matters. Of course there are bad analogies, including, as you imply, those deliberately chosen so as to throw away relevant detail, however one can still improve such analogies rather than reject them -- let alone all analogies -- out of hand.
Not only are they tools for arguments -- proof by existence -- but they are frequently useful tools for resolving arguments, precisely because they can help choose which are the important details in the real scenario.
"Your analogy can be improved by <insert idea>" is also simply more friendly than "all analogies are terrible" or even "your analogy is terrible", which is something to bear in mind if you enjoy friendly debates.